Vibrations in mechanical systems can have adverse consequences, such as fatigue, failure, and noise. Vibration suppression is achieved by passive or active methods. While active methods reduce vibrations in real time by making use of sensors and actuators, passive methods exploit the inherent ability of viscoelastic materials such as polymers to absorb and dissipate vibration energy. The Maxwell model, which comprises an elastic element (spring) and a viscous element (dashpot) in series, illustrates damping: for high frequency vibrations the Maxwell model predicts almost perfect elastic behavior, i.e., minimal energy dissipation, as the motion of the dashpot becomes negligible. For low or moderate frequencies the time scales of the viscoelastic relaxation and vibration are comparable, and they interfere destructively with one another, allowing for more efficient energy dissipation and damping.
Mechanical damping materials remove energy from a system. Motions to be damped can be periodic and regular (e.g., sine wave, square wave) or they can be irregular. Often a single mechanical event must be damped. Such an event is termed a shock, and the mechanical damping is termed shock absorption. Most damping measurements apply a periodic deformation to the article being tested, but it is also possible to assess the damping characteristics of a material from a single shock.
The Young's modulus, E, (also known as elastic modulus, modulus of elasticity, or tensile modulus) is a measure of the stiffness of a material. E is the ratio between the tensile stress, σ, divided by the tensile strain, e. E is typically measured on a tensile apparatus which elongates a material and reports the stress needed to produce a certain strain. Alternatively, a sample is compressed and the required stress for a needed deformation is measured. E may be measured under static, or quasi-static, conditions, where the stress does not vary with time. Alternatively, the modulus can be measured under dynamic or time-varying conditions where a material may exhibit properties of elasticity and viscous flow (viscoelasticity) in which case the modulus depends on frequency of deformation and a complex modulus, E*, is defined, where E*=E1+iE2, where E1 is the storage modulus, which is measure of energy stored on a deformation cycle, and E2 is the loss modulus, which is a measure of the energy lost on a cycle.
The shear modulus, G, (also referred to as the modulus of rigidity) of a material, measured under dynamic or time-varying conditions, is the ratio of the shear stress to the shear strain. The shear modulus is typically measured with a parallel-plate rheometer. If the shear rate changes, G depends on the frequency at which the shear changes. Therefore, a complex shear modulus is defined as G*=G1+iG2, where G1 is the storage modulus, which is a measure of energy stored on a deformation cycle, and G2 is the loss modulus, which is a measure of the energy lost on a cycle. For isotropic materials, E=3G for small deformations. For the present purposes, a material with low E is termed “soft” while a material with low G is termed “flowable.”
The ratio E1/E2 or G1/G2 is equal to tan(Δ), the ratio of energy lost to energy stored in one cycle. Tan(Δ) is called the loss factor and is a measure of damping efficiency, with greater damping indicated by higher tan(Δ).
Damping or shock-absorbing properties are not determined from static measurements. Damping properties are ascertained by time varying or periodic deformation of the sample. Thus, a soft material (low E) is not necessarily a good candidate for damping. Furthermore, a material that is effective for damping over a certain frequency range may not be effective for damping over another frequency range. Therefore, in reporting a complex modulus (E* or G*), a frequency or frequency range is preferably specified.
Recent studies have evaluated the static mechanical properties of polyelectrolyte multilayers, which are ultrathin films of complexed polyelectrolytes. See, for example, Jaber, J. A. and Schlenoff, J. B., J. Am. Chem. Soc. 128, 2940-2947 (2006). Polyelectrolyte multilayers are intermolecular blends of positively and negatively charged polyelectrolyte, wherein each layer of polyelectrolyte added to a growing film has an opportunity to complex efficiently and completely with the existing material, excluding the maximum amount of water. The elastic modulus of these films ranges from kPa to MPa. However, these films are far too thin (a few micrometers or less) to be used for mechanical components in most systems. Furthermore, the dynamic mechanical properties of molecularly blended complexes of positive and negative polyelectrolytes have not been evaluated. Polyelectrolyte complexes are prepared in a straightforward manner by mixing solutions of positive and negative polyelectrolytes.
The maximum amplitude of mechanical damping of an article generally depends on the physical dimensions of the article. Thus, there is a need to prepare articles with dimensions in the millimeter to centimeter scale to absorb the shock of mechanical vibrations on the millimeter scale. While a polyelectrolyte complex is easily prepared by mixing solutions of individual polyelectrolytes well, the precipitate is gelatinous and difficult to process. The dried complexes, for example, are generally infusible and therefore cannot be injection molded or reformed into articles under elevated temperatures. See Michales, A. S., J. Industrial Engin. Chem. 57, 32-40 (1965).
Polyelectrolyte complexes have been proposed as tissue engineering scaffolding (e.g., see Lim and Sun, Science, 210:908-910 (1980) and Yu et al., U.S. Pat. No. 6,905,875). The purpose of a tissue engineering scaffold is to support and maintain growing cells. Thus, these scaffolds are usually soft and porous and, therefore, not well suited for use as a compressive mechanical support. A tissue engineering scaffold is typically designed, prepared and employed without designing or expecting a particular damping property.